PARALLEL ARCHITECTURES FOR INAGE PROCESSING
Stanley R. Sternberg
Environmental Research I n s t i t u t e of Michigan
Ann Arbor, Michigan
Abs t rac t - Image process ing opera t ions a r e defined
which permit image process ing algorithms t o b e
w r i t t e n as a lgeb ra i c express ions whose va r i ab le s
are whole images. Highly p a r a l l e l computing a rch i -
t e c t u r e s f o r eva lua t ing these expressions are
presented.
Conventional computers do no t r e a d i l y lend
themselves t o p i c t u r e processing. D i g i t a l image
manipulation by conventional computer is accom
p l i shed only a t a tremendous cos t i n t i m e and con-
ceptua l d i s t r a c t i o n . Computer image process ing is
the a c t i v i t y of modifying a p i c t u r e such t h a t re-
t r i e v a l of r e l evan t p i c t o r i a l l y encoded informa-
t i o n becomes t r iv ia l . Algorithm development f o r
image process ing is an a l t e r n a t i n g sequence of
i n sp i r ed c rea t ive v i s u a l i z a t i o n s of des i r ed pro-
cessed r e s u l t s and the formal procedures imple-
menting t h e des i red process on a p a r t i c u l a r image
processing system. But our process of c r e a t i v e
v i s u a l i z a t i o n is of p i c t u r e s as a whole. Imple-
mentation of t h e v i sua l i zed image manipulation by
conventional computer r equ i r e s fragmentation of
t he p i c t o r i a l concept i n t o information u n i t s
matched t o t h e word o r i en ted capabi l i t ies of
genera l purpose machines. Conventional computer
image process ing could be broadly ca tegor ized as
manipulation of p i x e l states r a t h e r than p i c t o r i a l
content.
The image process ing approach presented i n
t h i s paper d i f f e r s from conventional methods i n
t h a t t h e b a s i c manipulative informat iona l u n i t is
p i c t o r i a l . Image process ing is t r e a t e d as a com-
pu ta t ion involv ing images as va r i ab le s i n a lgeb ra i c
expressions. These expressions may combine s e v e r a l
images through both l o g i c a l and geometric r e l a t ion -
sh ips . F ina l ly , h ighly e f f i c i e n t p a r a l l e l computer
a r c h i t e c t u r e s are proposed f o r implementing t h e
computation au tomat ica l ly .
The b inary image is t h e fundamental u n i t of
p i c t o r i a l information. A b ina ry image is a p i c t u r e
which is p a r t i t i o n e d i n t o reg ions of foreground and
background. By convention, foreground reg ions are
colored b lack , background reg ions are colored white.
A b inary image i n Euclidean twospace is an unbounded
p l ana r composition of in t e r lock ing b l ack and white
regions.
A b inary image formulation is a r u l e f o r
ass igning the co lo r s b l ack and whi te t o every po in t
X, y i n the plane. A b inary image is normaLly des-
c r ibed by a formulation which s p e c i f i e s t h e loca-
t i o n of a l l of i ts b lack poin ts . A b inary image i s
f u l l y spec i f i ed by t h e set of i t s b lack po in t s .
A b inary image t ransformat ion i s a r u l e f o r
mapping one b inary image i n t o another b inary image.
A b inary image opera t ion is a r u l e f o r mapping an
ordered p a i r of b inary images i n t o a b inary image.
Binary image opera t ions combine b inary images.
Binary image transformations and opera t ions
are e i t h e r l o g i c a l o r geometric. I f t he co lor of
a po in t P i n t h e r e s u l t a n t image can be fo rau la t ed
from t h e co lo r s of po in t P i n the transformzd o r
combining images, then the t ransformat ion o r opera-
t i o n is log ica l . Otherwise, it i s geometri:.
Geometric opera t ions on b inary images add and
s u b t r a c t po in t s v e c t o r i a l l y .
plane i s the sum o r d i f f e rence of t h e po in t s
(xl, Y,) and (x,, Y,) if P = (xl + x2, yl + Y,) o r
P = (xl - x, y1 - y,) r e spec t ive ly .
Complement is t h e l o g i c a l t ransformat ion of a
b inary image which in te rchanges t h e r o l e s of fore-
ground and background by exchanging the co lo r s
b lack and white. Re f l ec t ion is t h e geometric t rans-
formation which reverses t h e o r i e n t a t i o n of a b inary
image by ass igning t h e co lo r b lack t o a po in t P i n
t h e r e f l e c t e d image, i f and only i f t h e po in t -P is
b lack i n t h e b inary image undergoing r e f l e c t i o n .
Ref lec t ion of p l ana r b inary images r o t a t e s them 180
degrees about t h e i r o r i g i n o r t u rns them upside
down.
A po in t P i n the
Union and i n t e r s e c t i o n are t h e l o g i c a l opera-
t i o n s on b inary images. A po in t is b lack i n the
union of a p a i r of b inary images, i f and only i f i t
is b lack i n e i t h e r . A po in t is b lack i n the i n t e r -
s e c t i o n of two b inary images, i f and only i f i t is
b lack i n both.
D i l a t ion and e ros ion are t h e geometric opera-
A po in t P is b lack i n t h e t i o n s on b inary images.
d i l a t i o n of an ordered p a i r of b inary images, i f
and only i f t he re e x i s t s a b lack po in t i n t h e f i r s t
and a b lack po in t i n t h e second whose sum i s P. A
po in t P is b lack i n t h e e ros ion of an ordered p a i r
of b inary images, i f and only i f f o r every black
po in t i n the second t h e r e e x i s t s a b lack po in t i n
the f i r s t , such t h a t t h e i r d i f f e rence is P.
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